fix(agent): make Auto Mode auto-approve edits and shell commands

[posthog]

Problem

A customer reported PostHog Code "asking for lots of permissions allow this and that even when I have auto mode on." Auto Mode is labelled "Use a model classifier to approve/deny permission prompts", implying hands-off approval, but its allow-set (AUTO_ALLOWED_TOOLS.auto) only contained the base read/search/web/agent tools. Bash, BashOutput, KillShell, Edit, Write, and NotebookEdit fell through canUseTool to a manual prompt on every call, so users had to babysit each edit and shell command despite the mode promising the opposite.

Why: The mode's behavior didn't match what it advertises, which read as broken and drove a frustrated paying-customer ticket. (The broader complaints in that ticket — delays, errors, chat not starting — are upstream LLM-gateway capacity degradation and not fixable in this repo.)

Changes

• Add WRITE_TOOLS and BASH_TOOLS to the auto allow-set so Auto Mode auto-approves file edits and shell commands hands-off. MCP tools stay gated separately (do_not_use denied, needs_approval still prompts), so auto remains narrower than bypassPermissions.
• Correct the misleading "model classifier" description to "Auto-approve file edits and shell commands" in both the agent and core mode definitions, since the host's canUseTool arbiter can't re-defer to the SDK classifier for these tools.

How did you test this?

• Added parameterised unit tests in permission-handlers.test.ts verifying Auto Mode auto-allows Bash/BashOutput/KillShell/Edit/Write/NotebookEdit without prompting, and that Default Mode still prompts for them.
• vitest run on the touched test files (permission-handlers: 25 passed, execution-mode: 2 passed).
• pnpm --filter @posthog/agent typecheck clean; biome lint clean on changed files.

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

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Created with PostHog Code from an inbox report.

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit 041eeee.}